We say that an algebra is zero-product balanced if ab⊗c and a⊗bc agree modulo tensors of elements with zero-product. This closely related to but more general than the notion a determined introduced developed by Brešar, Villena others. Every surjective, preserving map from automatically weighted epimorphism, this implies algebras are their linear structure. Further, commutator subspace can be de...

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

Let π : E → B be a fiber bundle with fiber having the mod-2 cohomology algebra of a real or a complex projective space and let π ′ : E ′ → B be vector bundle such that Z2 acts fiber preserving and freely on E and E ′ − 0, where 0 stands for the zero section of the bundle π ′ : E ′ → B. For a fiber preserving Z2-equivariant map f : E → E ′ , we estimate the cohomological dimension of the zero se...

In this note we construct strange attractors in a class of skew product dynamical systems. A dynamical system of the class is a bundle map of a trivial bundle whose base is a compact metric space and the fiber is the non-negative half real line. The map on the base is a homeomorphism preserving an ergodic measure. The fiber maps either are strictly monotone and strictly concave or collapse at z...

In recent work Cheon, Han, Lee, Ryu, and Stehlé presented an attack on the multilinear map of Coron, Lepoint, and Tibouchi (CLT). They show that given many low-level encodings of zero, the CLT multilinear map can be completely broken, recovering the secret factorization of the CLT modulus. The attack is a generalization of the “zeroizing” attack of Garg, Gentry, and Halevi. We first strengthen ...

In this paper, we describe linear maps between complex Banach algebras that preserve products equal to fixed elements. This generalizes some important special cases where the elements are zero or identity element. First show if such map preserves a finite-rank operator, then it must also product. several instances, is enough product preserving be scalar multiple of an algebra homomorphism. Seco...